The grades on a language midterm at Loyola are normally distributed with $\mu = 75$ and $\sigma = 4.0$. Jessica earned a n $82$ on the exam. Find the z-score for Jessica's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Jessica's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{82 - {75}}{{4.0}}} $ ${ z \approx 1.75}$ The z-score is $1.75$. In other words, Jessica's score was $1.75$ standard deviations above the mean.